Incremental construction of three-dimensional objects having premachined rod elements and method for forming the same

ABSTRACT

A three-dimensional article and a method of manufacturing it, said article comprising individual increments in the form of rods that are premachined or preformed and assembled in registry, said rods being precut to discrete lengths, one end of each rod forming an increment of a precalibrated surface contour, each incremental surface being located in an optimum plane tangent to the precalibrated surface, the rod lengths and the cutting angles for the individual rods being determined by numerical control techniques.

United States Patent 1191 Bogart et al.

14 1 Mar. 27, 1973 [54] ,INCREMENTAL CONSTRUCTION OF THREE-DIMENSIONALOBJECTS HAVING PREMACHINED ROD ELEMENTS AND METHOD FOR FORMING THE SAMEInventors: Harold N. Bogart, Farmington; Norman W. Hopwood, Jr.,Dearborn, both of Mich.; Archie A. Pearson,

Tryon, N.C.; Foster E. Whitacre, Farmington, Mich.

Assignee: Ford Motor Company, Dearbom,

Mich.

Filed: Nov. 5, 1970 Appl. No.: 87,198

Related U.S. Application Data Division of Ser. No. 749,685, Aug. 2,1968, Pat. No. 3,605,528.

US. Cl ..72/475, 76/107 R, 425/DIG. 30 Int. Cl ..B21d 37/14, B2lk 5/20Field of Search ..72/470,

[56] References Cited UNITED STATES PATENTS 1,336,388 4/1920 Youngberg..72/475 2,332,360 10/1943 Wakefield..... ...76/l07 R 2,691,905 10/1954Onksen ..76/107 R Primary Examiner-Charles W. Lanham AssistantExaminerR. M. Rogers Attorney-John R. Faulkner and Donald J. Harrington[57] ABSTRACT A three-dimensional article and a method of manufacturingit, said article comprising individual increments in the form of rodsthat are premachined or preformed and assembled in registry, said rodsbeing precut to discrete lengths, one end of each rod forming anincrement of a precalibrated surface contour, each incremental surfacebeing located in an optimum plane tangent to the precalibrated surface,the rod lengths and the cutting angles for the individual rods beingdetermined by numerical control techniques.

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whim [WM W/ W {V} 4 2m I NCREMENTAL CONSTRUCTION OF THREE- DIMENSIONALOBJECTS HAVING PREMACHINED ROD ELEMENTS AND METHOD FOR FORMING THE SAMEGENERAL DESCRIPTION OF THE INVENTION This application is a division ofcopending application Ser. No. 749,685 filed Aug. 2, 1968, now US. Pat.No. 3,605,528. That application is assigned to the assignee of theinstant application.

Our invention is related generally to the manufacture ofthree-dimensional objects, such as metal forming dies, although theteachings of our invention can be applied also to construction of otherobjects such as die casting dies, plastic molds and other objects ofvarious geometry.

It is possible also to employ the teachings of our invention in formingobjects that are related indirectly to the metal forming art. Examplesof such objects might be tooling aid devices, fixtures and objects whichmight otherwise be formed by casting techniques.

We prefer to use metal rods of hexagonal shape in building a die orother article. The rods are precut to length using a numericallycontrolled cut-off machine, the ends of each of the rods forming surfaceincrements that are optimally tangent to a curved surface contour of aprecalibrated surface. The point of tangency between the incrementaltangent surface and the curved surface is located at the rod center.

An automated, numerically-controlled identification and assemblyprocedure makes it possible to identify individual rods and to positionthem in proper registry with the rod ends forming the equivalent of aroughmachined surface for a casting.

The individual rods may be bonded together by brazing, diffusionbrazing, adhesive bonding, chemical bonding or other bonding proceduresto form a solid section. The section then can be finish machined to arequired surface contour.

In the case of a metal forming die, the upper die section and the lowerdie section can be formed simultaneously. The basic procedure usedduring the numerically controlled rod cutting step produces registeringelements of the upper and lower die sections, the matching ends of thetwo rods forming increments of the rough machined die surface equivalentfor their respective die sections. The die surface angle formed duringeach angular cut for the rod for one die section is necessarily theproper die surface angle for the corresponding rod for the remainingcomplementary die section.

The numerical definition of the finished die surface is determined withcomputer assisted data processing steps. The surface itself is normallydefined initially in two dimensions on a surface layout, although othertechniques have been used. A series of points on character lines andsection lines on the two-dimensional surface draft is translated byinterpolation into a mathematically continuous surface. With aid of acomputer, a network of mathematically computed points in space can beobtained with sufficient density so that the points define the finishedsurface in three dimensions.

Tangent vectors for each of the points thus computed can be determinedby partial differentials with reference to each of two coordinateplanes. Having determined these vectors, a surface normal can bedetermined mathematically by using, for example, a cross-product method.It is this normal vector that determines the cutting angle for the diesurface end of the rod, and the point at which each normal is determined is made to correspond to a point lying on the axis of theindividual rod. Where compound curvature precludes a unique commonplane, the center in translated to assure sufficient machining stock.Similarly, the location of extreme angles, determined to be still in sawrange, are adjusted for variations in saw kerf.

The computed data is prepared with known data processing procedures andused to generate a control tape which is adapted for controlling anumericallycontrolled cut-off machine. Intelligence stored in the tapeincludes data necessary to obtain the proper rod length for each of theindividual rods, the die surface angle for each of the rod ends, and theidentification number for each rod. It is desirable to side-stripe therods to assist in orientation during final assembly.

It is possible to include rods of different hardness in the completeddie. Rods of varying chemical composition may be used to providevariable wear resisting qualities in selected areas of the die surfaceif this is desired. In this instance the preprocessing steps in the dataprocessing procedure for preparing the control tape can be modified toinclude necessary instructions to provide material selection at theoutset before the angular cuts are made.

It is possible also under some circumstances to use rods other thanhexagonal rods. For example, triangular rods, rods with trapezoidalcross sections or rods with cross sections in the shape of modifiedsquares or parallelograms also may be used. The rods should have,however, a self-orienting feature in order to permit a registry thatestablishes structural rigidity.

Although the instant disclosure is directed to a construction for ametal forming die and to a method for making them, correspondingprocedural steps can be used also to form objects other than metalforming dies, such as die casting dies, casting equivalents of objectssuch as fixtures, certain tooling aids, machine bases, et cetera.

In making a numerical definition of the die surface, a process drawingis prepared concurrently with the numerical processing of the panelsurface. This includes all the lines necessary to describe the surface.Each line is given an identifying number on the drawing. The numberedlines on the drawing then are identified on a body draft, showing thesurface in orthogonal representation. The lines necessary to describethe surface are superimposed on the body draft. All lines are digitizedand used as raw input data for the computer assisted processing steps.The mathematical equations of the characteristic lines then aredetermined, which information is used to develop a matrix of points inspace.

Other factors necessary for the building of the incremental die,including holes, edges or other special conditions such as the size andshape of the bars, the symmetry or lack of symmetry of the die then aredetermined.

Special regions of the die may be defined if this is necessary. Forexample, it may be necessary to use a stop-off material to preventbrazing or adhering of certain incremental rods at one location, but notat another. Also the rods may be required to be shortened at onelocation, or removed, or elongated. Different rod material in certainregions might be required. The line enclosing the region in questionmust be defined numerically, and the relationship of that line to theother character lines on the surface must be determined.

Information regarding identification of therods in certain regions mustalso be determined numerically. Such information must includeinstructions for slabbing or grooving of the corners of the rod orpermanent.

numbering of the rods.

A two-dimensional grid of points representing the corners and centers ofall the rods required to make up the incremental die is determined. Thepoints on this grid then are projected onto the numerical definition ofthe die surface which already is determined, as explained above, therebyproviding three-dimensional data and surface normal data.

After the rods are cut and oriented, a reading head scans theidentification of the individual rods and identifies the pieces of therods. Odd numbered pieces are channeled in one direction, and evennumbered pieces are channeled in another direction. This in effectseparates the hex rod elements into complementary groups, which are theprincipal components of the punch half of the die sections and theprincipal components of the die half of the die sections.

Following this stage, both the odd numbered pieces and the even numberedpieces are arranged in numerical order. This operation is automatedunder numerical control. If the numerical arrangement is interrupted byreason of a missing piece, a gap in the row will appear and a signallingdevice will alert the operator so that the missing piece may be locatedand inserted in the gap, thus allowing a continuous flow of rods. Ifnecessary, a dummy piece may be inserted into the gap thereby allowingoperation to continue. The dummy then can be replaced in an off-lineoperation with an actual rod.

After the rods are arranged in numerical order, they are assembled intoa fixture of special height, width, and depth to permit assembly of allthe rods for the particular die half involved. All of the faces of therods that are identified by slabbing are oriented in a common direction.

The automated portion of the system may be a transfer line type ofmachine into which the raw material in the form of the hex bar stock canbe introduced and fed through the several stations. Changes occur inthis raw material in progressive stages, as explained above, as it istransferred from one station to the next. It finally emerges from theterminal end of the system as hex rod elements of varying dimensionalcharacteristics. The-processing that occurs at the servo stations isinitiated and controlled primarily through the use of numerical data,although this is supported by automatic cycling devices.

The numerical data is the result of the merging of the process datarequired for the incremental die and the numerical representation of thedie surface, as indicated in the schematic diagram of FIG. 1.

BRIEF DESCRIPTION OF THE FIGURES OF THE DRAWINGS FIG. 1 is a schematicdiagram of the method steps used in making incremental metal formingdies.

FIG. 2 is a plan view of an assembled incremental die.

FIG. 3 is a cross section view taken along the plane of section line3-3, FIG. 2.

FIG. 4 is a cross sectional view taken along the plane of section line4-4 of FIG. 2.

FIG. 5 is an isometric, sectional view taken along the plane of sectionline 5-5 of FIG. 2.

FIG. 6 is a cross sectional, geometric representation of a die surfaceformed by the ends of the rods, the ends being situated in planes thatare tangent to the finished surface contour at the location of the rodcenter lines. It is taken along the plane of section line 66 of FIG. 8.

FIG. 7 is a cross sectional view of cooperating upper and lower diesections of a metal forming die, the plane of the section being parallelto the center lines of the incremental rods.

FIG. 8 is a partial plan view of the incremental rods of FIG. 7 as seenfrom the plane of section line 8-8 of FIG. 7.

FIGS. 9A, 9B and 9C is a process flow chart showing the method forconstructing a numerically-controlled, incremental, rough-machinedcasting equivalent.

FIG. 10 shows a typical machine base made in a form of a hexagonal rodconstruction.

FIG. 11 is an automotive fender stamped form a die of the typeillustrated in FIG. 7.

PARTICULAR DESCRIPTION OF THE INVENTION In FIGS. 2, 3, 4 and 5 we haveillustrated one of two die sections for forming sheet metal. In thisinstance, the die section has a cooperating die surface in the form of aconcavity. The cooperating die section would have a convex die surfacethat would register with the concavity of the die section of FIG. 2.

Numeral 10 designates in FIG. 2 a die housing, which may be in the formof a steel box. The housing may be of any shape desired although in theFIG. 2 embodiment it is square.

Situated in the housing in close registry are hexagonal rods 12. Eachrod is cut to form an upper surface, such as that shown at 14, whichgenerally cooperates with an adjacent end surface of the adjacenthexagonal rod. The surfaces directly adjacent surface 17 are designatedby reference characters 16, 18, 20 and 22 in FIG. 5. The height of eachrod as well as the angularity of the end surfaces are chosen so thateach individual surface forms an increment of a larger surface having acontour that approximates the contour of the desired finished diesurface.

In the embodiment shown in FIGS. 2, 3, 4 and 5, the row of hexagonalrods directly adjacent the vertical walls of the housing 10 defines apilot ridge 24 which extends around the periphery of the die section.Each individual rod is formed with a segment of the ridge 24 so thatwhen the individual segments are joined sideby-side they define theperipheral ridge 24. This ridge registers with a peripheral groove inthe registering die section so that the die sections are piloted, onewith respect to the other, into perfect registry.

When the die sections are brought together into registry, eachincremental end surface of each rod 12 registers with a cooperating endsurface of a companion rod for the other die section. The angle of thesurface for any given rod 12 in the die section of FIG. 5, for example,would have an identical angle on the cooperating end surface for thecompanion rod of the other die section. A clearance space between thesetwo end surfaces accommodates the metal thickness of the sheet metalthat is worked by the dies.

In FIG. 7 we have shown in cross section form a pair of die sections,each having a die surface that registers with the die surface of itscompanion section. The space between the companion end surfaces of theupper and lower rod segments of the upper die section 27 and lower diesection 29 is occupied by the sheet metal 25.

The die sections shown in FIG. 7 have been finish machined to providecontinuous, smooth, die surfaces. This machining process employsnumerically-controlled, multiple-axis, milling machines in a mannerdescribed in co-pending application Ser. No. 577,997, filed Sept. 8,1966, which is assigned to the assignee of this invention. Reference maybe had to application Ser. No. 577,997 for the purpose of supplementingthis disclosure.

Prior to the finish machining operation, each end of the hexagonal rodsforms an end surface that is tangent to the die surface contour at apoint that falls on the center lineof the rod itself. This isillustrated in FIG. 6 where the individual rods 12 include surfaces 26,28 and 30 which form tangent planes for the die surface contour shown at32. The points of tangency for the surfaces 26, 28 and 30 coincide withthe points of intersection of the center lines 34, 36 and 38 for therods 12 with the finished die surface 32. The region between the surface32 shown in FIG. 6 and the individual tangent planes provided by thesurfaces 26, 28 and 30 represents excess metal that is removed duringthe finish machining operation. The tangent planes themselvesapproximate the contour 32 after the rods are assembled in registry.This is the equivalent of a roughmachined casting of the die section.

It is not necessary, as in the case of finish machining of cast diesections, to remove large quantities of metal during the machiningoperation. No rough machining is required. Only a single finishmachining operation is needed to transform the approximate surfacecontour provided by the tangent planes of the rod end surfaces. into thefinished contour represented by reference character 32.

The surface designated by reference character 32 in FIG. 6 shouldcorrespond to the mathematically determined surface defined by thecomputed points in space described in the preamble portion of thisspecification. Suitable flowlines, or proportionately defined lines onthe surface 32 can be computed by mathematically interpolatingappropriate points on the specified surface.

The tangent vectors at any point along the surface to be machined can bedetermined readily by the expedient of determining a partial derivativeof the equation of a line of intersection between the computed surfacecontour and a plane parallel to one of the coordinate planes. Anothertangent vector containing that same point can be determined with respectto another coordinate plane. Having these two tangent vectors, it ispossible to obtain the unit normal vector. The center of the cuttingtool can be adjusted accordingly along the unit normal vector so thatthe cutting tool itself always machines a tangent plane at any givenpoint on the computed surface.

The machine control may include an automatic parabolic interpolator thatrequires the simultaneous definition of the three coordinates of thepoints. Having received the three coordinates of selected points in itscontrol system, the milling cutter, several of which are known in theindustry, will direct the cutting tool to machine the surface 32 throughthe three points along a parabolic are rather than along straight linesegments between the points.

The information necessary to obtain this unit normal vector can be usedalso with modified computer subroutines to determine the normals for theincremental end surfaces of the rod which in turn determine the angle ofthe cutting tool that cuts the individual rod segments and the angularposition of the rods during the cutting operation.

In FIGS. 9A, 9B and 9C we have shown a process flow chart for variousmachining operations and the assembly procedures necessary to converthexagonal bar stock into a finished pair of matching die sections forworking sheet metal. The chart should be read from left to right. Thevarious process steps have been indicated in the upper portion of theview of FIGS. 9A, 9B and 9C; and the corresponding functions have beenillustrated in the sketches in the lower portion. The sketches and themethod steps of the block diagram have been related by correspondingnumbers.-

The assembly procedure has been divided into 13 stages, each stage beingidentified by a Roman Numeral character. Between each of the stages thefinal product of the previous stage is transferred and reloaded forentry into the next stage. Which may take place at a different physicallocation.

At the outset, a turret capable of accommodating hexagonal rods isloaded. If the particular die under consideration requires areas ofvarying hardness, rods of varying hardness are entered at this stage.Rods of differing alloy content also may be used. Automatic feeders canbe provided for feeding the hexagonal rod stock to the turret. Apreprogrammed control tape is provided with information which will causethe numerical control system to command the exact angular adjustment ofthe turret that will permit proper material selection as designated inthe sketch of step I. After the turret position is such that a propermaterial is conditioned for advancement through the turret, the rod isadvanced against a fixed stop. As the stop is withdrawn, a cutting toolmoves across the plane of the raw bar stock as indicated in step number4 for stage I. A tail stock, which is situated in alignment with theturret,

then is adjusted to a proper X-axis position. The

amount of the adjustment depends on the preprogrammed instruction thatis provided to the control system by the programmed tape. Each rod, ofcourse, will have its discrete position determined at step 5. It isdifferent for each rod, unless, of course, the die section required rodsof constant length. After the X-axis position is determined for the tailstock, the bar cut in step 4 is fed into the tail stock as indicated instep 6. At that time the rod is cut to length by a cut-off tool asindicated in step 7. The cut rod now becomes an inprocess hex rod whoselength represents the adjusted, computed length resulting from thecomputer program.

The cut rod is transferred and loaded into a fixture to permit millingcutters, operating in' tandem, to form a flat on one side of the hexrod. The rod is clamped and fed into a stop to establish a suitableposition for one of the milling cutters. The other milling cutter isadjustable in the direction of the X-axis indicated in stage II, theamount of the adjustment depending upon the length of the rod involved.

The milling cutter adjustment is necessary to accommodate varyinglengths of rods, and it is made in response to computed data. Themachined flats provide a convenient area for impression stamping anidentification number at each end of the rod such that the metal raisedaround the characters will be below the original surface of the materialwhere it will not cause interference preventing surface-to-surfacecontact of the rods after assembly.

The machined rod then is transferred again and loaded into anotherfixture as indicated in stage III. Identifying binary codes are punchedon the flats that are machined in stage II. This code identifies a rodso that it can be assembled in its proper registry with the adjacentrods in the final assembly.

The bar is automatically positioned against an end stop and clamped. Onemarking head is fixed and the other is adjustable in response to thecommand of the numerical control system to accommodate the spreadbetween the flats previously machined. The identifying numbers areconsecutive from end to end and progressive from rod to rod. 1

After the identifying marks have been impressed on the milled flats ateach end of the rod, the ends of the rods are chamfered by chamferingtools that are advanced into the rod along the rod axis as indicated instep 2 of stage III.

The chamfering operation can be automated. It does not requireinstructions from the numerical control tape. Further, each of thetransfer and loading operations can be fully automated independently ofthe numerical data in the control tape.

The selection of the material in stage I and the positioning of the tailstock to a discrete length in stage I also requires instructions fromnumerical control tape, although the other functions in stage I can befully automated independently of the numerical data. It is consideredpractical operation to establish groups of similar length bars duringthe previous computation to simplify this operation. Alternatively,maximum yield from standard bar lengths could be obtained by optimizedgrouping.

The chamfered and milled rod then is transferred and loaded into apreoriented collect indicated in stage IV. The collet is oriented aboutthe A axis in response to numerical control data since it must becapable of receiving a rod in its proper angular position with referenceto the position orienting reference angle that accounts for the positionof the milled flat ends.

If the particular rod involved requires a flat side, the proper flat canbe machined at this stage. This is done by feeding the rod through thepreoriented collet into the path of motion of a milling cutter, theX-axis position of which is determined by numerical data in addition tothe X-axis position of the cutter, it is necessary to properly orientthe angular position of the rod prior to the machining. This isindicated in the step 2 in stage IV. This adjustment also occurs inresponse to numerical control instructions provided by the control tape.

If the rod does not need milling, of course, this stage can be omitted.Milling may be needed, for example, when it is desired to provide anaxial passage in the finished die to permit entry of a temperaturecontrolling media or lubricant, or to provide desired discontinuities inthe surface.

The machined rod then is transferred to an automated transfer and loaddevice and received by a preoriented collet in stage V. The angularposition of the collet is determined with numerical data.

A cutter blade in the cut-off machine is adjusted as indicated in step 2in stage V to a proper angle, 0, with respect to the center line of therod. The rod then is adjusted in the X-axis direction as indicated instep 3 of stage V. This stage requires feeding of the rod through thepreoriented collet shown in step 1 of stage V until it engages a stop,and then determining the angular position of the blade and the X-axisposition of the rod. The rod is cut as indicated in step 4. This formstwo rod segments, one of which will form an element of one die sectionand the other of which will form a complementary element of a companiondie section. The cutting itself can be fully automated, although theangular positioning of the blade, the X-axis adjustment of the rod andthe angular orientation of the collet each require instructions in theform of numerical data.

The cut pieces are transferred through an automated transfer and loadingdevice and received by appropriate mounting fixtures at stage VI wherean automated wire brushing operation removes flash and burrs from thecut edges of the rods. After the rods are wire brushed they may betransferred to an automated conveyor. Selected rods are received then bya degreasing apparatus if this stage is desired, which immerses the rodsinto a degreasing liquid bath. The rods also may be grit blasted ifrequired.

The grit blast and the degreasing steps can be fully automated steps,but the copper spray step requires numerical data instructions sinceunder some circumstances it might be desired to apply stop-offmaterialinstead of the spray copper. This is desired if a copper braze for thatrod is to be avoided. For example, if an opening is desired in thefinished surface contour at the location normally occupied by aparticular rod, that rod may be withdrawn if it is not bonded to itsadjacent rods.

The rods then are transferred to a station which will permit orientationof the rods with a scanner operation whereby the identification numberson the rod ends can be read by a reading head. This occurs, asindicated, in stage X. The rods then are separated into odd and evennumbers and are arranged in numerical sequence. The odd numbered rodsare arranged in an assembly that defines one die section, and the evennumbered rods are assembled to form the other die section. The assembledrods are indicated in stage XIII. The assembled rods of FIG. 9Ccorrespond to the assembly indicated in FIGS. 2, 3, 4 and 5.

This overall operating procedure is illustrated schematically in summaryfashion in FIG. 1. A numerical representation of the die surface is oneingredient of the numerical data required by the numerical system thatcontrols the various process steps. In addition to the numericalrepresentation of the die surface, the numerical system also requiresprocess data necessary to adapt the numerical system for an incrementaldie program. That includes information derived from the surface normalsdescribed with reference to the points in space that define the diesurface, which information is used to establish the cutter angle instage V as well as the orientation of the collet in stage V which holdsthe rod during the cutting operation. In addition to this, the addedprocess data must be sufficient to enable the cutoff machine to locatethe proper X-axis adjustment for the rod parts.

The output data for the system is derived after the two process datainputs are integrated. The output data is used to perform the variousfunctions indicated by the legends in FIG. 1.

Having described a preferred form of our invention, what we claim anddesire to secure by US. Letters Patent is:

1. A pair of rough machined casting equivalents for cooperating diesections, each comprising a plurality of incremental rods with a crosssection in the form of a regular polygon, said rods being situated inregistry and bonded together to define an integral assembly,corresponding ends of said rods forming discrete twodimensionalsurfaces, the end surfaces of one assembly being contiguous to define apredetermined, threedimensional die surface contour, the end surfaces ofthe rods of the other assembly being contiguous to define apredetermined die surface contour, concave portions of one surfacecontour registering with and being similar to the convex portions of theother surface contour, each of the incremental rods of one die sectionbeing aligned with a companion rod in the other die section, the unitnormal vector for the end surface of each of the rods of one die sectionbeing parallel to the unit normal vector for the adjacent end of thecompanion rod of the other die section whereby the die surface contourfor one section is complementary to the die surface contour of the otherdie section.

2. The combination as set forth in claim 1 wherein each of theincremental rods of one die section is aligned with a companion rod inthe other die section, the unit normal vector for the end surface ofeach of said rods of one section being parallel to the unit normalvector for the adjacent end of the companion rod of the other diesection whereby the die surface contour for one section is complementaryto the die surface contour of the other die section.

3. The combination as set forth in claim 2 wherein said rods in crosssection form a regular hexagon whereby said rods may be nested togetherto form an integral assembly.

1. A pair of rough machined casting equivalents for cooperating diesections, each comprising a plurality of incremental rods with a crosssection in the form of a regular polygon, said rods being situated inregistry and bonded together to define an integral assembly,corresponding ends of said rods forming discrete two-dimensionalsurfaces, the end surfaces of one assembly being contiguous to define apredetermined, threedimensional die surface contour, the end surfaces ofthe rods of the other assembly being contiguous to define apredetermined die surface contour, concave portions of one surfacecontour registering with and being similar to the convex portions of theother surface contour, each of the incremental rods of one die sectionbeing aligned with a companion rod in the other die section, the unitnormal vector for the end surface of each of the rods of one die sectionbeing parallel to the unit normal vector for the adjacent end of thecompanion rod of the other die section whereby the die surface contourfor one section is complementary to the die surface contour of the otherdie section.
 2. The combination as set forth in claim 1 wherein each ofthe incremental rods of one die section is aligned with a companion rodin the other die section, the unit normal vector for the end surface ofeach of said rods of one section being parallel to the unit normalvector for the adjacent end of the companion rod of the other diesection whereby the die surface contour for one section is complementaryto the die surface contour of the other die section.
 3. The combinationas set forth in claim 2 wherein said rods in cross section form aregular hexagon whereby said rods may be nested together to form anintegral assembly.